Using implicit differentiation find dy/dx at the point (1,1) if:

Question

-4x^2 + y(x) + x^2 y(x)^4 + 2 =0

Answer 1

We differentiate both sides of given equation: - 8x + y' + 2xy⁴ + 4x²y³y' = 0; y'(1 + 4x²y³) = 8x - 2xy⁴.

Now y' = (8x - 2xy⁴)/(1 + 4x²y³). At point (1, 1) y' =(8 - 2)/(1 + 4) = 6/5